Construction of a parametric invariant hypergraph model for integrating and analyzing multi-context educational data

Abstract

This study examines multi-context educational data acquired from independent digital platforms and characterized by differences in the composition of entities, types of interactions, and data representation schemes. The task addressed relates to the lack of a unified model for the invariant representation of heterogeneously structured data, the assessment of their structural compatibility, the determination of the costs of mutual adaptation, and the possibility of comparative analysis of digital platforms while preserving the characteristics of the educational context. A parametrically typed invariant hypergraph model has been proposed, which represents educational data as typed hypergraphs, their semantic normalization into a single type space, as well as the calculation of indicators of structural invariance, adaptation, and integral utility. A parametric analysis of sensitivity to changes in the data structure and model weighting coefficients has been suggested. The novelty of this work is underscored by the following: – a unified parametric hypergraph model has been constructed that combines the invariant representation of educational data, a quantitative assessment of the structural compatibility, adaptation costs, and integral utility of digital educational platforms; – a parametric analysis has been proposed to examine the influence of structure and weighting factors on the integration and comparative analysis of platforms; – the model was experimentally tested on data from independent educational platforms, including over 3,100 educational records and 4,861 hyperedges, revealing differences in the structural compatibility of the studied contexts. The model supports decision making in the selection and design of digital educational ecosystems in the context of structurally heterogeneous data